Related papers: From Wires to Cosmology
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on…
A brief review of the modern state of quantum cosmology is presented as a theory of quantum initial conditions for inflationary scenario. The no-boundary and tunneling states of the Universe are discussed as a possible source of probability…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
Friction is ubiquitous in daily life, from nanoscale machines to large engineering components. By probing the intricate interplay between system parameters and frictional behavior, scientists seek to unveil the underlying mechanisms that…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
We investigate static and dynamic topologies of a 2-mode real world university-industry cooperation network. Due to its large size and complex structure, we choose to use statistical proxies for this goal. Among the findings, we shall call…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
Cosmic strings are predicted in many models beyond the Standard Model of particle physics. In models which admit strings, a network of strings will inevitably be formed in a phase transition in the early universe and will persist to the…
Universe structure emerges in the unreduced, complex-dynamic interaction process with the simplest initial configuration (two attracting homogeneous fields, quant-ph/9902015). The unreduced interaction analysis gives intrinsically creative…
Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle…
This thesis is dedicated to the study of inflationary scenarios based on string theory. Inflation is a brief period of accelerated expansion in the very early Universe which gives natural explanations for problems of the Standard Big Bang…
Nonlinear electrodynamics with two dimensional parameters is studied. The range of electromagnetic fields when principles of causality, unitarity and the classical stability hold, are obtained. A singularity of the electric field at the…
We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes…
We analyze observational signatures arising from an epoch in cosmology corresponding to the simple harmonic universe, which consists of positive curvature, a negative cosmological constant, and one or more exotic matter sources with $-1 < w…
The initial conditions describing seed fluctuations for the formation of structure in standard cosmological models, i.e.the Harrison-Zeldovich distribution, have very characteristic ``super-homogeneous'' properties: they are statistically…
All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with…
Reconstructing the initial conditions of the universe is a key problem in cosmology. Methods based on simulating the forward evolution of the universe have provided a way to infer initial conditions consistent with present-day observations.…